Bayesian multiple comparisons in Freund's bivariate exponential populations with type I censored data

Abstract We consider two components system which have Freund’s bivariate exponentialmodel. In this case, Bayesian multiple comparisons procedure for failure rates is sug-gested in K Freund’s bivariate exponential populations. Here we assume that the com-ponents enter the study at random over time and the analysis is carried out at someprespeci ed time. We derive fractional Bayes factor for all comparisons under non-informative priors for the parameters and calculate the posterior probabilities for allhypotheses. And we select a hypotheses which has the highest posterior probability asbest model. Finally, we give a numerical examples to illustrate our procedure.Keywords: Bayesian multiple comparison, fractional Bayes factor, noninformative pri-ors, posterior probability. 1. Introduction Freund (1961), Marshall and Olkin (1967), Block and Basu (1974) and many authorsformulated a bivariate extension of the exponential model as a model for a system wherethe lifetimes of the two components may depend on each other. In particular, the Freund’smodel has been generalized in the literature in various ways. Some of the generalizationsare based on various functional representations of Freund’s model obtained by replacingexponential random variables by other random variables. Let (X;Y) be random variablesof a Freund’s bivariate exponential model with parameters = ( ;